Question

which radical expression is equivalent to $b^{\frac{2}{3}}$? choose 1 answer: a $\frac{2}{\sqrt3{b}}$ b $(\sqrt3{b})^2$ c $\frac{\sqrt2{b}}{\sqrt3{b}}$ d $\sqrt2{b^3}$

Explanation:

Step1: Recall the exponent - radical relationship

The general formula for converting a rational exponent to a radical is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}\), where \(n\) is the index of the radical and \(m\) is the power of the base or the power of the radical.

For the expression \(b^{\frac{2}{3}}\), here \(a = b\), \(m = 2\) and \(n=3\).

Step2: Apply the formula

Using the formula \(a^{\frac{m}{n}}=(\sqrt[n]{a})^{m}\), when \(a = b\), \(m = 2\) and \(n = 3\), we get \(b^{\frac{2}{3}}=(\sqrt[3]{b})^{2}\)

Answer:

B. \((\sqrt[3]{b})^{2}\)